Abstract

Stochastic optimization serves as a central tool for effective population management. We present an impulse control model and a related singular control model for finding the cost-effective and sustainable population management policies of fish-eating birds, predators of fishery resources. The impulse control model considers the cost proportional to the amount of the killed bird and the fixed cost, while singular counterpart considers only the proportional cost. Their optimal controls are discussed from both qualitative and quantitative viewpoints.

Keywords

Stochastic optimization Impulse control Singular control Threshold-type population management

Notes

Acknowledgements

This paper is partly funded by grants-in-aid for scientific research No. 16KT0018, No. 17J09125, and No. 17K15345 from the Japan Society for the Promotion of Science (JSPS) and Applied Ecology Research Grant No. 2016-02 from Water Resources Environment Center in Japan. The authors thank officers of Hirose Fisheries Cooperatives for their useful comments and suggestions.

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